1. Field of the Invention
The present invention relates to a digitally controlled oscillator and in particular to a digitally controlled oscillator having a high resolution in frequency tuning.
2. Description of the Related Art
A digitally controlled oscillator (DCO) is a circuit used for generating a periodic signal of a frequency controlled by a digital control word. FIG. 1A depicts a prior art DCO 100A comprising a pair of cross-coupled N-channel metal oxide semiconductor (NMOS) transistors M1 and M2 configured as a positive feedback loop between a first output node VO1 and a second output node VO2, a pair of inductors L1 and L2 configured as a load to the transistors M1 and M2, and a varactor array 110 shunt between outputs (or drain terminals) of the transistors M1 and M2 to provide a tunable capacitance. In FIG. 1A, VDD denotes a first fixed-potential circuit node and VSS denotes a second fixed-potential circuit node.
The varactor array 110 comprises N varactor pairs (e.g., a first pair {101, 102}, a second pair {111, 112}, a third pair {121, 122}, and so on), wherein N is an integer. A varactor is a special type of capacitor with a capacitance determined by a voltage applied to it. FIG. 1B depicts a typical transfer characteristic for capacitance as a function of applied voltage for a varactor. As the applied voltage increases, the capacitance of the varactor approaches a minimum value Cmin. As the applied voltage decreases, the capacitance of the varactor approaches a maximum value Cmax. Thus, application of a sufficiently high voltage or a sufficiently low voltage can be used to attain the minimum capacitance value Cmin or the maximum capacitance value Cmax of the varactor.
In FIG. 1A, the varactor array 110 receives an N-bit control word D[N−1:0] comprising N control bits. Each control bit is either logically 1 (i.e., a sufficiently high voltage) or logically 0 (i.e., a sufficiently low voltage) and is used to control one respective varactor pair. Each varactor pair comprises a first varactor and a second varactor. The first varactor is connected to the first output node VO1 on one end and to a control bit on the other end. The second varactor is connected to the second output node VO2 on one end and to the same control bit on the other end. For instance, the first varactor pair {101, 102} comprises a first varactor 101 and a second varactor 102; the first varactor 101 is connected to the first output node VO1 on one end and to the control bit D[0] on the other end; and the second varactor 102 is connected to the second output node VO2 on one end and to the same control bit D[0] on the other end. In this manner, a total effective capacitance of the varactor array 110 is tunable between N·Cmin/2 and N·Cmax/2, inclusively, with a step size of (Cmax−Cmin)/2. Here, the divide by two expression (/2) accounts for the fact that the two varactors in each varactor pair are connected in series and therefore the total capacitance, as seen by the differential signal defined by the two output nodes VO1 and VO2, is halved.
The varactor array 110 and the two inductors L1 and L2 form a resonator circuit with a resonant frequency that roughly determines an oscillating frequency of the DCO 100A. The pair of cross-coupled NMOS transistors M1 and M2 provides a gain to sustain the oscillation, but has little influence on the oscillating frequency. Therefore, the oscillating frequency of the DCO 100A is tunable between approximately ½π√{square root over (L·N·Cmax)} and ½π√{square root over (L·N·Cmin)}, wherein L denotes an inductance value for the inductors L1 and L2.
The DCO 100A has a frequency tuning resolution limited by (Cmax−Cmin)/2 (i.e., an incremental change in the total effective capacitance of the varactor array 110). Theoretically, one can use very small varactors to make the incremental change (Cmax−Cmin)/2 very small and thus achieve a high resolution. In practice, however, a manufacturing process will always impose a constraint on minimum dimensions allowed for a device. For a typical CMOS process as of nowadays technology, for instance, an incremental capacitance change for a varactor array can be in the order of magnitude of femto-Farads (fF or 10−15 F). In many applications, a corresponding resolution in frequency tuning is not very high. What is needed is a method of extending a frequency tuning of a DCO.